High-dimensional Regression with a Count Response
By Zilberman & Abramovich
Introduction
- The paper focus in regression for count high-dimensional data using GLMs like Poisson or NB.
- For this reason, LASSO techniques have been proposed for high-dimensional settings in Poisson and negative binomial regression. However, the theoretical ground for high-dimensional count data has been less developed.
Introduction
- General purpose of the paper.
- They proposed a penalized maximum likelihood estimator with theoretical guarantees (adaptive minimaxity).
- Develop computationally feasible methods (convex surrogates) for practical application.
- Evaluate performance via simulations and real data.
Paper Structure
- Theoretical Framework. It defines the statistical models (Poisson, NB), proposes the penalized estimation method and provides its statistical properties.
- Practical Solutions & Analysis: The paper explores LASSO and SLOPE as convex surrogates. It analyzes their theoretical properties, showing SLOPE can retain optimality under specific conditions.
- Empirical Evaluation: The performance of the practical methods (LASSO, SLOPE) is assessed and compared through simulations and real-world dataset.